TITLE

AUTHOR(S)
Calanchi, Marta; Ruf, Bernhard
PUB. DATE
May 2010
SOURCE
Calculus of Variations & Partial Differential Equations;May2010, Vol. 38 Issue 1/2, p111
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
We discuss existence and non-existence of positive solutions for the following system of Hardy and Hï¿½non type: ["Multiple line equation(s) cannot be represented in ASCII text"] where O ? 0 is a bounded domain in RN , N = 3, p, q > 1, and a, ï¿½ > -N. We also study symmetry breaking for ground states when O is the unit ball in RN.
ACCESSION #
49024225

## Related Articles

• ESSENTIAL NORM OF EXTENDED CESÃ€RO OPERATORS FROM ONE BERGMAN SPACE TO ANOTHER. HU, ZHANGJIAN // Bulletin of the Australian Mathematical Society;Apr2012, Vol. 85 Issue 2, p307

Let Ap(Ï†) be the pth Bergman space consisting of all holomorphic functions f on the unit ball B of â„‚n for which $\f\^p_{p,\varphi }= \int _B f(z)^p \varphi (z) \,dA(z)\lt +\infty$, where Ï† is a given normal weight. Let Tg be the extended...

• Sobolev-type Lp-approximation orders of radial basis function interpolation to functions in fractional Sobolev spaces. Lee, Mun Bae; Lee, Yeon Ju; Yoon, Jungho // IMA Journal of Numerical Analysis;Jan2012, Vol. 32 Issue 1, p279

Sobolev-type error analysis has recently been intensively studied for radial basis function interpolation. Although the results have been very successful, some limitations have been found. First, the spaces of target functions are not large enough for thecase 1â‰¤pâ‰¤âˆž to be used...

• Solutions for a class of iterated singular equations. Çetinkaya, A.; Özalp, N. // Proceedings of the Indian Academy of Sciences: Mathematical Scie;May2007, Vol. 117 Issue 2, p259

Some fundamental solutions of radial type for a class of iterated elliptic singular equations including the iterated Euler equation are given.

• Widths of classes of finitely smooth functions in Sobolev spaces. Kudryavtsev, S. // Mathematical Notes;Mar/Apr2005, Vol. 77 Issue 3/4, p494

We describe the weak asymptotics of the behavior of the Kolmogorov, Gelfand, linear, Aleksandrov, and entropy widths of the unit ball of the space WHw ( Id) in the space W( Id).

• L error estimates for approximation by Sobolev splines and Wendland functions on â„. Ward, John // Advances in Computational Mathematics;May2013, Vol. 38 Issue 4, p873

It is known that a Green's function-type condition may be used to derive rates for approximation by radial basis functions (RBFs). In this paper, we introduce a method for obtaining rates for approximation by functions which can be convolved with a finite Borel measure to form a Green's...

• RADIAL BASIS FUNCTION INTERPOLATION IN SOBOLEV SPACES AND ITS APPLICATIONS. MAnping Zhang // Journal of Computational Mathematics;Mar2007, Vol. 25 Issue 2, p201

In this paper we study the method of interpolation by radial basis functions and give some error estimates in Sobolev space Hk (Î©) (k â‰¥ 1). With a special kind of radial basis function, we construct a basis in Hk(Î©) and derive a meshless method for solving elliptic partial...

• Multiscale analysis in Sobolev spaces on bounded domains with zero boundary values. Townsend, Alex; Wendland, Holger // IMA Journal of Numerical Analysis;Jul2013, Vol. 33 Issue 3, p1095

Compactly supported radial basis functions can be used to define multiscale approximation spaces. A multiscale scheme is studied for the approximation of Sobolev functions on bounded domains with restricted data sites. Our method employs compactly supported radial basis functions with centres at...

• Closed form representations for a class of compactly supported radial basis functions. Hubbert, Simon // Advances in Computational Mathematics;Jan2012, Vol. 36 Issue 1, p115

In this paper we re-examine Wendland's strategy for the construction of compactly supported positive definite radial basis functions. We acknowledge that this strategy can be modified to capture a much larger range of functions, including the so-called missing Wendland functions which have been...

• Compactness and existence results in weighted Sobolev spaces of radial functions. Part I: compactness. Badiale, Marino; Guida, Michela; Rolando, Sergio // Calculus of Variations & Partial Differential Equations;Sep2015, Vol. 54 Issue 1, p1061

Given two measurable functions $$V(r )\ge 0$$ and $$K(r)> 0$$ , $$r>0$$ , we define the weighted spaces and study the compact embeddings of the radial subspace of $$H_{V}^{1}$$ into $$L_{K}^{q_{1}}+L_{K}^{q_{2}}$$ , and thus into $$L_{K}^{q}$$ ( $$=L_{K}^{q}+L_{K}^{q}$$ ) as a particular case....

Share